The residual source estimator is an a posteriori spatial discretization error estimator wehave developed. Demonstrated for a DGFEM-0 scheme (piecewise constant in space), theestimator exhibited accuracy and precision at a fraction of the computational cost of anh-refinement estimator. However, a piecewise linear scheme (DGFEM-1) is more in linewith contemporary transport applications, prompting a separate investigation.The residual approximation and derivative recovery procedures are outlined for DGFEM-1,and the resultant error estimate is compared to a Method of Manufactured Solutionsgeneratedreference solution. The distributions of effectivity indices (the ratio of estimatedto true error) are compared to those acquired by the DGFEM-0 error estimate and andh-refinement estimator.Because the convergence of the numerical solution, which is used to generate the aposteriori estimate by recovering derivatives of order higher than those comprising theDGFEM-1 space, is affected by solution order and mesh regularity, increasing the solutionorder can have negative effects. Since we restrict our reference solutions to be eitherdiscontinuous across singular characteristics or to have first derivatives discontinuousacross singular characteristics, reflecting physically real scenarios, the DGFEM-1 solutionmoments are not accurate enough to give as good a residual source error estimate asDGFEM-0. This is contrasted to an h-refinement error estimate, which outperforms itsDGFEM-0 results. Methods are proposed to generate convergent derivative approximationsdespite the adverse effects of singular characteristics.
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